Is it possible to bulk lock a tag field?

You can use multi-select in the web UI or a Plex Desktop app to do this. In any of the views (whichever makes sense for your use case) select multiple items.

For tracks, select items using the empty circle in the far-left column when you hover over a track. For artists or albums, select the empty circle in the top-left of the poster when you hover over an item.

Once the items are selected, click the edit (pencil) icon at the top of the list. In the tags tab you can then click the lock next to the field(s) you want to lock.

(You can also use shift-click to select multiple items in a contiguous list at the same time.)

But to answer your question, yes, this could be scripted as well. I’ll see if I can find an example for you (at least for something similar). I’m pretty sure there’s a Python script on these forums showing how to lock movie posters in bulk.

[Edit]
This is what I was thinking of.